Is it possible to calculate the center of an incomplete sphere?
The shipped add-on tinyCAD has a 'Resurrect Circle Center' operation, which finds the circumcenter of a triangle of 3 vertices.
If you select 3 vertices from your sphere-section, which lie on one of the sphere's great circles, it will place the 3D cursor at the center of the complete sphere, and draw the great circle in the plane of the vertices.